It has a slightly deceiving name: it's not a palm, but rather a succulent. The large trunk holds water during drought, and makes it a rather forgiving and tolerant plant.
Bright light conditions are ideal, but not essential. Like you've heard everyone say about the tiny green succulents, you should allow this one to dry out between waterings and they actually grow best when slightly root bound. Ponytail palms don’t need frequent repotting. Really, they could go for years without needing a larger pot.